COLD FORMED STEEL STRUCTURES

LECTURES PREPARED BY:PROF. DR. Abdelrahim Khalil Dessouki

Lecture 2

2INFLUENCE OF COLD WORK ON MECHANICAL PROPERTIES OF STEEL

The mechanical properties of cold-formed sections are sometimes substantiallydifferent from those of the steel sheet, strip, plate, or bar before forming.

Why ?

To explain why, let us look at the following slides:

3Effect of cold work on mechanical properties in cold-formed steel sections(a) Channel section.

4Effect of cold work on mechanical properties in cold-formed steel sections(b) Joist chord.

5The influence of cold work indicate that the changes of mechanical properties due to cold work are caused mainly by strain hardening and strain aging, as illustrated in Fig. below:

Effects of strain hardening and strain aging on stressstrain characteristics.

6This leads to: Increase the yield strength. Increase the ultimate strength. Decrease the ductility.

7Effect of Cold Work on The Material Yield Strength

Investigating the influence of cold work, Karren derived the following equations for the ratio of corner yield strength to virgin yield strength:

8With regard to the full-section properties, the tensile yield strength of the full section may be approximated by using a weighted average as follows:

Example 1: Determine the average tensile yield point of steel Fya for theflange of a given channel section to be used as a beam (Fig. below). Considerthe increase in strength resulting from the cold work of forming. Use the AISISpecification and A653 SS Grade 40 steel (Fy = 40 ksi and Fu = 55 ksi).

9 1. Check North American 1. Check North American SpecificationsSpecifications Requirements.Requirements.

A. In order to use Eq. (2.14) for computing the average tensile yield point for the beam flange, the channel must have a compact compression flange, that is r =1.0.

Assume that on the basis of Arts. 3.5.1, 3.5.2, and 3.5.3, the reduction factor is found to be unity, then Eq. (2.14) can be used to determine Fya.

B. When Eq. (2.11) is used to determine the tensile yield point of corners Fyc , the following three requirements must be satisfied:

Fuv/Fyv >1.2, R/t < 7, < 120 Since the actual values are Fuv /Fyv = 55/40 = 1.375, R/t =0.1875/0.135 = 1.389, and = 90, which all satisfy the North North American SpecificationsAmerican Specifications requirements, Eq. (2.11) can be used to determine Fyc.

10

2. Calculation of 2. Calculation of FFycyc. According to . According to EqEq. (2.11),. (2.11),

whereBc = 3.69(Fuv /Fyv ) - 0.819(Fuv /Fyv )2 - 1.79 = 1.735 m = 0.192(Fuv /Fyv ) - 0.068 = 0.196Therefore,

3. Calculation of 3. Calculation of FFyaya. By using . By using FFycyc = 65.08 = 65.08 ksiksi, , FFyfyf = virgin = virgin yield point = 40 yield point = 40 ksiksi, and, and

11

The above value of Fya can be used for tension and compression flanges.It represents a 16% increase in yield stress as compared with the virginyield stress of steel.

Example 2.2: Determine the average yield point of steel Fyafor the axially loaded compression member, as shown in Fig. 2.10. Consider the increase in strength resulting from the cold work of forming. Use A570 Grade 33 steel (Fy = 33 ksi and Fu = 52 ksi).

Solution1. Check North American SpecificationsNorth American Specifications

Requirements.A. Determination of reduction factor.Assume that on the basis of Arts. 3.5.1, 3.5.2, and 3.5.3, the reductionfactor r is found to be unity,then Eq. (2.14) can be used to determine Fya.

12

B. Review of Fuv /Fyv , R/ t, and Fuv /F uv = 52/33 =1.576 > 1.2 (OK) R/t = 0.1875/0.135 = 1.389 < 7 (OK) = 90o < 120o (OK)

Therefore, Eq. (2.11) can be used to compute Fyc.

2. Calculation of Fyc. From Eq. (2.11),

Bc = 3.69(Fuv /Fyv ) - 0.819(Fuv/Fyv )2 - 1.79 = 1.991 m = 0.192(Fuv /Fyv ) - 0.068 = 0.235

and

13

3. Calculation of Fya. By usingF yc = 60.82 ksiF yf = 33 ksi

C = total corner area / total area of full section= 8(0.054) / 2.54 = 0.17

andFya = C F yc + (1-C) Fyf = 37.73 ksi < Fuv (OK)

The above computed Fya represents a 14% increase in yield point when the strength increase from the cold work of forming is considered only for the corners. In the Canadian specification, Eq. (2.15) next slide is used to compute the average tensile yield point Fy of the full section of tension or compression members. This simpler equation is also applicable for the full flange of flexural members.

14

where D = number of 90o corners. If other angles are used, D is the sum of the bend angles divided by 90o.

W* = ratio of the length of centerline of the full flange of flexural members, or of the entire section of tension or compression members,to the thickness t.

Example 2.3 For the channel section used in Example 2.1, determine the average yield point of steel Fy for the beam flange by using Eq. (2.15). Solution. Based on the type of steel and the dimensions used in Example 2.1,the following values can be obtained:F y =40 ksiF u =55 ksiD = 2

15

This value provides a good agreement with the value of Fya = 46.37 ksicomputed in Example 2.1 on the basis of the AISI Specification.

Example 2.4 For the I-section used in Example 2.2, determine the averageyield stress of steel Fy for the compression member. Use Eq. (2.15).

Solution. By using the data given in Example 2.2, the following values canbe used :

16

F y= 33 ksiF u = 52 ksiD = 2(4) = 8

17

RESIDUAL STRESSES DUE TO COLD FORMING

Residual stresses are stresses that exist in the member as a result of manufacturing and fabricating processes. In the past, the distribution of residual stresses and the effect of such stresses on the load-carrying capacity of steel members have been studied extensively for hot-rolled wide-flange shapes andwelded members. For these structural shapes, the residual stresses are caused by uneven cooling after hot rolling or welding. These stresses are often assumed to be uniform across the thickness of the member.

In the past, the residual stress distribution in cold-formed steel Members has been studied analytically and experimentally by a number of investigators. Figure 2.14,next slidenext slide adapted fromRef. 2.26, shows Ingvarssons measured residual stresses in the outer and inner surfaces of a channel section.

18

Figure 2.14 (a) : Measured longitudinal residual stress distribution in outer surfaces of COLD-FORMED steel channels.

19

Figure 2.14 (b) : Measured longitudinal residual stress distribution in inner surfaces of COLD-FORMED steel channels.

20

The average measured residual stresses for the same channel section are shown in Fig. 2.15. It is expected that the effect of such stresses on the stressstrain relationship of cold-formed members is similar to that for hot-rolled shapes, even though for the former, the residual stress results from cold rolling orcold bending.

In the design of cold-formed steel members, the AISI buckling Provisions have been written for a proportional limit that is considerably lower than then yield point of virgin steel. The assumed proportional limit seems justified for the effect of residual stresses and the influence of cold work discussed inSection 2.7.

Figure 2.15 is shown in next slide as follows:

21

INFLUENCE OF COLD WORK ON MECHANICAL PROPERTIES OF STEELThe influence of cold work indicate that the changes of mechanical properties due to cold work are caused mainly by strain harEffect of Cold Work on The Material Yield Strength